Thin Fe/Cr multilayered films are the most intensively investigated system with regard to the recently discovered giant magnetoresistance (GMR). In order to contribute to the understanding of this effect, we present the results of resistance measurements during growth of Fe/Cr single-layer and multilayer films. We determined the transport parameters of these films and compared the thickness dependent conductances of ferromagnetic and antiferromagnetic coupled layers. The difference in the conductances shows complete saturation for Fe thicknesses above 3 nm and is consistent with the ex situ measured GMR of the antiferromagnetic film. This points to interface scattering as origin of the GMR. With respect to this result we investigated the influence of the interface roughness on the amount of GMR.